Null Model and Simulation

The nullmodel function creates an object, which can serve as a basis for Null Model simulation via the simulate method. The update method updates the nullmodel object without sampling (effective for sequential algorithms). smbind binds together multiple simmat objects.

Usage

nullmodel(x, method)
# S3 method for class 'nullmodel'
print(x, ...)
# S3 method for class 'nullmodel'
simulate(object, nsim = 1, seed = NULL,
    burnin = 0, thin = 1, ...)
# S3 method for class 'nullmodel'
update(object, nsim = 1, seed = NULL, ...)
# S3 method for class 'simmat'
print(x, ...)
smbind(object, ..., MARGIN, strict = TRUE)

Arguments

x: A community matrix. For the print method, it is an object to be printed.
method: Character, specifying one of the null model algorithms listed on the help page of commsim. It can be a user supplied object of class commsim.
object: An object of class nullmodel returned by the function nullmodel. In case of smbind it is a simmat object as returned by the update or simulate methods.
nsim: Positive integer, the number of simulated matrices to return. For the update method, it is the number of burnin steps made for sequential algorithms to update the status of the input model object.
seed: An object specifying if and how the random number generator should be initialized ("seeded"). Either NULL or an integer that will be used in a call to set.seed before simulating the matrices. If set, the value is saved as the "seed" attribute of the returned value. The default, NULL will not change the random generator state, and return .Random.seed as the "seed" attribute, see Value.
burnin: Nonnegative integer, specifying the number of steps discarded before starting simulation. Active only for sequential null model algorithms. Ignored for non-sequential null model algorithms.
thin: Positive integer, number of simulation steps made between each returned matrix. Active only for sequential null model algorithms. Ignored for non-sequential null model algorithms.
MARGIN: Integer, indicating the dimension over which multiple simmat objects are to be bound together by smbind. 1: matrices are stacked (row bound), 2: matrices are column bound, 3: iterations are combined. Needs to be of length 1. The other dimensions are expected to match across the objects.
strict: Logical, if consistency of the time series attributes ("start", "end", "thin", and number of simulated matrices) of simmat objects are strictly enforced when binding multiple objects together using smbind. Applies only to input objects based on sequential null model algorithms.
...: Additional arguments supplied to algorithms. In case of smbind it can contain multiple simmat objects.

Details

The purpose of the nullmodel function is to create an object, where all necessary statistics of the input matrix are calculated only once. This information is reused, but not recalculated in each step of the simulation process done by the simulate method.

The simulate method carries out the simulation, the simulated matrices are stored in an array. For sequential algorithms, the method updates the state of the input nullmodel object. Therefore, it is possible to do diagnostic tests on the returned simmat object, and make further simulations, or use increased thinning value if desired.

The update method makes burnin steps in case of sequential algorithms to update the status of the input model without any attempt to return matrices. For non-sequential algorithms the method does nothing.

update is the preferred way of making burnin iterations without sampling. Alternatively, burnin can be done via the simulate method. For convergence diagnostics, it is recommended to use the simulate method without burnin. The input nullmodel object is updated, so further samples can be simulated if desired without having to start the process all over again. See Examples.

The smbind function can be used to combine multiple simmat objects. This comes handy when null model simulations are stratified by sites (MARGIN = 1) or by species (MARGIN = 2), or in the case when multiple objects are returned by identical/consistent settings e.g. during parallel computations (MARGIN = 3). Sanity checks are made to ensure that combining multiple objects is sensible, but it is the user's responsibility to check independence of the simulated matrices and the null distribution has converged in case of sequential null model algorithms. The strict = FALSE setting can relax checks regarding start, end, and thinning values for sequential null models.

Value

The function nullmodel returns an object of class nullmodel. It is a set of objects sharing the same environment:

data:: original matrix in integer mode.
nrow:: number of rows.
ncol:: number of columns.
rowSums:: row sums.
colSums:: column sums.
rowFreq:: row frequencies (number of nonzero cells).
colFreq:: column frequencies (number of nonzero cells).
totalSum:: total sum.
fill:: number of nonzero cells in the matrix.
commsim:: the commsim object as a result of the method argument.
state:: current state of the permutations, a matrix similar to the original. It is NULL for non-sequential algorithms.
iter:: current number of iterations for sequential algorithms. It is NULL for non-sequential algorithms.

The simulate method returns an object of class simmat. It is an array of simulated matrices (third dimension corresponding to nsim argument).

The update method returns the current state (last updated matrix) invisibly, and update the input object for sequential algorithms. For non sequential algorithms, it returns NULL.

The smbind function returns an object of class simmat.

Author

Jari Oksanen and Peter Solymos

Note

Care must be taken when the input matrix only contains a single row or column. Such input is invalid for swapping and hypergeometric distribution (calling r2dtable) based algorithms. This also applies to cases when the input is stratified into subsets.

Examples

data(mite)
x <- as.matrix(mite)[1:12, 21:30]

## non-sequential nullmodel
(nm <- nullmodel(x, "r00"))
#> An object of class “nullmodel” 
#> ‘r00’ method (binary, non-sequential)
#> 12 x 10 matrix
#> 
(sm <- simulate(nm, nsim=10))
#> An object of class “simmat” 
#> ‘r00’ method (binary, non-sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> 

## sequential nullmodel
(nm <- nullmodel(x, "swap"))
#> An object of class “nullmodel” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Iterations = 0 
#> 
(sm1 <- simulate(nm, nsim=10, thin=5))
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> Start = 5, End = 50, Thin = 5
#> 
(sm2 <- simulate(nm, nsim=10, thin=5))
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> Start = 55, End = 100, Thin = 5
#> 

## sequential nullmodel with burnin and extra updating
(nm <- nullmodel(x, "swap"))
#> An object of class “nullmodel” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Iterations = 0 
#> 
(sm1 <- simulate(nm, burnin=10, nsim=10, thin=5))
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> Start = 15, End = 60, Thin = 5
#> 
(sm2 <- simulate(nm, nsim=10, thin=5))
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> Start = 5, End = 50, Thin = 5
#> 

## sequential nullmodel with separate initial burnin
(nm <- nullmodel(x, "swap"))
#> An object of class “nullmodel” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Iterations = 0 
#> 
nm <- update(nm, nsim=10)
(sm2 <- simulate(nm, nsim=10, thin=5))
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> Start = 15, End = 60, Thin = 5
#> 

## combining multiple simmat objects

## stratification
nm1 <- nullmodel(x[1:6,], "r00")
sm1 <- simulate(nm1, nsim=10)
nm2 <- nullmodel(x[7:12,], "r00")
sm2 <- simulate(nm2, nsim=10)
smbind(sm1, sm2, MARGIN=1)
#> An object of class “simmat” 
#> ‘r00’ method (binary, non-sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 10 
#> 

## binding subsequent samples from sequential algorithms
## start, end, thin retained
nm <- nullmodel(x, "swap")
nm <- update(nm, nsim=10)
sm1 <- simulate(nm, nsim=10, thin=5)
sm2 <- simulate(nm, nsim=20, thin=5)
sm3 <- simulate(nm, nsim=10, thin=5)
smbind(sm3, sm2, sm1, MARGIN=3)
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 40 
#> Start = 15, End = 210, Thin = 5
#> 

## 'replicate' based usage which is similar to the output
## of 'parLapply' or 'mclapply' in the 'parallel' package
## start, end, thin are set, also noting number of chains
smfun <- function(x, burnin, nsim, thin) {
    nm <- nullmodel(x, "swap")
    nm <- update(nm, nsim=burnin)
    simulate(nm, nsim=nsim, thin=thin)
}
smlist <- replicate(3, smfun(x, burnin=50, nsim=10, thin=5), simplify=FALSE)
smbind(smlist, MARGIN=3) # Number of permuted matrices = 30
#> An object of class “simmat” 
#> ‘swap’ method (binary, sequential)
#> 12 x 10 matrix
#> Number of permuted matrices = 30 
#> Start = 55, End = 100, Thin = 5 (3 chains)
#> 

if (FALSE) { # \dontrun{
## parallel null model calculations
library(parallel)

if (.Platform$OS.type == "unix") {
## forking on Unix systems
smlist <- mclapply(1:3, function(i) smfun(x, burnin=50, nsim=10, thin=5))
smbind(smlist, MARGIN=3)
}

## socket type cluster, works on all platforms
cl <- makeCluster(3)
clusterEvalQ(cl, library(vegan))
clusterExport(cl, c("smfun", "x"))
smlist <- parLapply(cl, 1:3, function(i) smfun(x, burnin=50, nsim=10, thin=5))
stopCluster(cl)
smbind(smlist, MARGIN=3)
} # }